回復 22# martinofncku 的帖子
第4題
分以下三種情形
(1)甲B班，乙A班
(2)甲B班，乙C班
(3)甲C班，乙A班
每種情形，另四人都有\({{3}^{4}}=81\)種分法
所求\(=81*3=243\)
第8題
\(\begin{align}
& \frac{\Delta ABD}{\Delta ACE}=\frac{\overline{BD}}{\overline{EC}} \\
& \frac{\frac{1}{2}\times \overline{AB}\times \overline{AD}\times \sin \angle BAD}{\frac{1}{2}\times \overline{AC}\times \overline{AE}\times \sin \angle CAE}=\frac{3}{4} \\
& \frac{\overline{AB}\times \overline{AD}}{\overline{AC}\times \overline{AE}}=\frac{3}{4}\quad \ldots \ldots \left( 1 \right) \\
& \\
& \frac{\Delta BAE}{\Delta CAD}=\frac{\overline{BE}}{\overline{DC}} \\
& \frac{\frac{1}{2}\times \overline{AB}\times \overline{AE}\times \sin \angle BAE}{\frac{1}{2}\times \overline{AC}\times \overline{AD}\times \sin \angle CAD}=\frac{5}{6} \\
& \frac{\overline{AB}\times \overline{AE}}{\overline{AC}\times \overline{AD}}=\frac{5}{6}\quad \ldots \ldots \left( 2 \right) \\
& \\
& \left( 1 \right)\times \left( 2 \right) \\
& \frac{{{\overline{AB}}^{2}}}{{{\overline{AC}}^{2}}}=\frac{5}{8} \\
& \frac{\overline{AB}}{\overline{AC}}=\frac{\sqrt{10}}{4} \\
\end{align}\)
